6. 1
If f(x) = 2x + 1 and g(x) = x
find [f g](x) and [g f](x)
o o
[f g](x)
o Domain:
Domain:
[g f](x)
o
7. EVEN FUNCTIONS
Graphically: A function is "even" if its graph is symmetrical about the yaxis.
These functions
are even...
These are
not ...
Symbolically (Algebraically)
a function is "even" IFF (if and only if) ƒ(x) = ƒ(x)
Examples: Are these functions even?
1. f(x) = x² 2. g(x) = x² + 2x
f(x) = (x)² g(x) = (x)² + 2(x)
f(x) = x² g(x) = x² 2x
since f(x)=f(x) since g(x) is not equal to g(x)
f is an even function g is not an even function
8. ODD FUNCTIONS
Graphically: A function is "odd" if its graph is symmetrical about the origin.
These
functions
These are
are odd ... not ...
Symbolically (Algebraically)
a function is "odd" IFF (if and only if) ƒ(x) = ƒ(x)
Examples: 1. ƒ(x) = x³ x 2. g(x) = x³ x²
ƒ(x) = (x)³ (x) g(x) = (x)³ (x)²
ƒ(x) = x³ + x g(x) = x³ x²
ƒ(x) = (x³ x) g(x) = (x³x²)
ƒ(x) = x³ + x g(x) = x³+ x²
since ƒ(x)= ƒ(x) since g(x) is not equal to g(x)
ƒ is an odd function g is not an odd function